Heteroskedastic Errors Research Articles

Integration of GSTARIMA Model with Heteroskedastic Error and Kriging for Climate Forecasting: A Systematic Review

Integration of GSTARIMA Model with Heteroskedastic Error and Kriging for Climate Forecasting: A Systematic Review

Estimating spatial autoregressions under heteroskedasticity without searching for instruments

This paper proposes estimating higher-order spatial autoregressions with spatial autoregressive errors and heteroskedastic error innovations without searching for instruments by explicitly exploiting the endogeneity of spatial lags in the outcome and error equations. The resulting estimator is shown to be consistent and asymptotically normal. Monte Carlo experiments demonstrate that it possesses better finite-sample properties than existing estimators. An empirical study of venture capital funding for biotechnology firms illustrates that spatial correlation stretches as far as 20 miles and that the number of venture capital firms in close proximity has stronger impact on the level of funding than as reported in an existing study.

Estimating conditional average treatment effects with heteroscedasticity by model averaging and matching

We propose a model averaging approach, combined with a partition and matching method to estimate the conditional average treatment effects under heteroskedastic error settings. The proposed approach has asymptotic optimality and consistency of weights and estimator. Numerical studies show that our method has good finite-sample performances.

The link between multiplicative competitive interaction models and compositional data regression with a total

ABSTRACT This article sheds light on the relationship between compositional data (CoDa) regression models and multiplicative competitive interaction (MCI) models, which are two approaches for modeling shares. We demonstrate that MCI models are particular cases of CoDa models with a total and that a reparameterization links both. Recognizing this relation offers mutual benefits for the CoDa and MCI literature, each with its own rich tradition. The CoDa tradition, with its rigorous mathematical foundation, provides additional theoretical guarantees and mathematical tools that we apply to improve the estimation of MCI models. Simultaneously, the MCI model emerged from almost a century-long tradition in marketing research that may enrich the CoDa literature. One aspect is the grounding of the MCI specification in assumptions on the behavior of individuals. From this basis, the MCI tradition also provides credible justifications for heteroskedastic error structures – an idea we develop further and that is relevant to many CoDa models beyond the marketing context. Additionally, MCI models have always been interpreted in terms of elasticities, a method that has only recently emerged in CoDa. Regarding this interpretation, the CoDa perspective leads to a decomposition of the influence of the explanatory variables into contributions from relative and absolute information.

Properties of the coefficient estimators for the linear regression model with heteroskedastic error term

In this paper we present estimated generalized least squares (EGLS) estimator for the coefficient vector β in the linear regression model y = βX + ε, where disturbance term can be heteroskedastic. For the heteroskedasticity of the changed segment type, using Monte-Carlo method, we investigate empirical properties of the proposed and ordinary least squares (OLS) estimators. The results show that the empirical covariance of the EGLS estimators is smaller than that of OLS estimators.

Generalized kernel regularized least squares estimator with parametric error covariance

A two-step estimator of a nonparametric regression function via Kernel regularized least squares (KRLS) with parametric error covariance is proposed. The KRLS, not considering any information in the error covariance, is improved by incorporating a parametric error covariance, allowing for both heteroskedasticity and autocorrelation, in estimating the regression function. A two step procedure is used, where in the first step, a parametric error covariance is estimated by using KRLS residuals and in the second step, a transformed model using the error covariance is estimated by KRLS. Theoretical results including bias, variance, and asymptotics are derived. Simulation results show that the proposed estimator outperforms the KRLS in both heteroskedastic errors and autocorrelated errors cases. An empirical example is illustrated with estimating an airline cost function under a random effects model with heteroskedastic and correlated errors. The derivatives are evaluated, and the average partial effects of the inputs are determined in the application.

A JACKKNIFE LAGRANGE MULTIPLIER TEST WITH MANY WEAK INSTRUMENTS

This paper proposes a jackknife Lagrange multiplier (JLM) test for instrumental variable regression models, which is robust to (i) many instruments, where the number of instruments may increase proportionally with the sample size, (ii) arbitrarily weak instruments, and (iii) heteroskedastic errors. In contrast to Crudu, Mellace, and Sándor (2021, Econometric Theory 37, 281–310) and Mikusheva and Sun (2021, Review of Economic Studies 89, 2663–2686), who proposed jackknife Anderson–Rubin tests that are also robust to (i)–(iii), we modify a score statistic by jackknifing and construct its heteroskedasticity robust variance estimator. Compared to the Lagrange multiplier tests by Kleibergen (2002, Econometrica 70, 1781–1803) and Moreira (2001, Tests with Correct Size when Instruments Can Be Arbitrarily Weak, Working paper) and their modification for many instruments by Hansen, Hausman, and Newey (2008, Journal of Business & Economic Statistics 26, 398–422), our JLM test is robust to heteroskedastic errors and may circumvent a possible decrease in the power function. Simulation results illustrate the desirable size and power properties of the proposed method.

Bayesian GARCH modeling of functional sports data

The use of statistical methods in sport analytics has gained a rapidly growing interest over the last decade, and nowadays is common practice. In particular, the interest in understanding and predicting an athlete’s performance throughout his/her career is motivated by the need to evaluate the efficacy of training programs, anticipate fatigue to prevent injuries and detect unexpected of disproportionate increases in performance that might be indicative of doping. Moreover, fast evolving data gathering technologies require up to date modelling techniques that adapt to the distinctive features of sports data. In this work, we propose a hierarchical Bayesian model for describing and predicting the evolution of performance over time for shot put athletes. We rely both on a smooth functional contribution and on a linear mixed effect model with heteroskedastic errors to represent the athlete-specific trajectories. The resulting model provides an accurate description of the performance trajectories and helps specifying both the intra- and inter-seasonal variability of measurements. Further, the model allows for the prediction of athletes’ performance in future sport seasons. We apply our model to an extensive real world data set on performance data of professional shot put athletes recorded at elite competitions.

A RMT-based LM test for error cross-sectional independence in large heterogeneous panel data models*

This paper introduces a new test for error cross-sectional independence in large panel data models with exogenous regressors having heterogenous slope coefficients. The proposed statistic, LMRMT , is based on the Lagrange Multiplier (LM) principle and the sample correlation matrix of the model’s residuals. Since in large panels poorly estimates its population counterpart, results from Random Matrix Theory (RMT) are used to establish the high-dimensional limiting distribution of LMRMT under heteroskedastic normal errors and assuming that both the panel size N and the sample size grow to infinity in comparable magnitude. Simulation results show that is largely correctly sized (except for some small values of N and T). Further, the empirical size and power outcomes show robustness of our statistic to deviations from the assumptions of normality for the error terms and of strict exogeneity for the regressors. The test has comparable small sample properties to related tests in the literature which have been developed under different asymptotic theory.

Structural change tests under heteroskedasticity: Joint estimation versus two‐steps methods

There has been a recent upsurge of interest in testing for structural changes in heteroskedastic time series, as changes in the variance invalidate the asymptotic distribution of conventional structural change tests. Several tests have been proposed that are robust to general form of heteroskedastic errors. The most popular use a two‐steps approach: first estimate the residuals assuming no changes in the regression coefficients; second, use the residuals to approximate the heteroskedastic asymptotic distribution or take an entire sample average to construct a test for which the variance process is averaged out. An alternative approach was proposed by Perron et al. (Perron et al. (2020). Quantitative Economics 11: 1019–1057) who provided a test for changes in the coefficients allowing for changes in the variance of the error term. We show that it transforms the variance profile into one that effectively has very little impact on the size of the test. With respect to the power properties, the two‐steps procedures can suffer from non‐monotonic power problems in dynamic models and in static models with a correction for serial correlation in the error. Most have power equals to size with zero‐mean regressors. Even when the two‐steps tests have power, it is generally lower than that of the latter test.

Bias-corrected method of moments estimators for dynamic panel data models

A computationally simple bias correction for linear dynamic panel data models is proposed and its asymptotic properties are studied when the number of time periods is fixed or tends to infinity with the number of panel units. The approach can accommodate both fixed-effects and random-effects assumptions, heteroskedastic errors, as well as higher-order autoregressive models. Panel-corrected standard errors are proposed that allow for robust inference in dynamic models with cross-sectionally correlated errors. Monte Carlo experiments suggest that under the assumption of strictly exogenous regressors the bias-corrected method of moment estimator outperforms popular GMM estimators in terms of efficiency and correctly sized tests.

Robust post-selection inference of high-dimensional mean regression with heavy-tailed asymmetric or heteroskedastic errors

We propose a robust post-selection inference method based on the Huber loss for the regression coefficients, when the error distribution is heavy-tailed and asymmetric in a high-dimensional linear model with an intercept term. The asymptotic properties of the resulting estimators are established under mild conditions. We also extend the proposed method to accommodate heteroscedasticity assuming the error terms are symmetric and other suitable conditions. Statistical tests for low-dimensional parameters or individual coefficient in the high-dimensional linear model are also studied. Simulation studies demonstrate desirable properties of the proposed method. An application to a genomic dataset about riboflavin production rate is provided.

The influence of the correlation-covariance structure of measurement errors over uncertainties propagation in online monitoring: application to environmental indicators in SUDS.

This paper presents a methodology to assess the influence of the correlation-covariance structure of measurement errors in online monitoring over the propagation of uncertainties, applied to wet-weather environmental indicators in sustainable urban drainage systems (SUDSs). The effect of auto-correlated and heteroskedastic errors in measured time-series over the estimated probability density function (PDF) of different environmental indicators is analyzed for a wide variety of possible error structures in the data. For this purpose, multiple correlation-covariance structures are randomly generated from exploring the parametric space of a linear exponent autoregressive (LEAR) model, employing a Bayesian-based Markov Chain Monte Carlo sampling technique. Significant differences tests are proposed to identify the most correlated parameters of the correlation-covariance error model with statistics of the environmental indicator PDFs. The method is applied to total suspended solids (TSS) and chemical oxygen demand (COD) time-series recorded during 13 rainfall events at the inlet and outlet of a SUDS train (stormwater settling tank-horizontal constructed wetland). In this case, results showed that the total error in the estimation of the analyzed environmental indicators is mostly explained by standard uncertainties (flattening of the PDFs) rather than bias contributions (displacement of the PDFs). The correlation-covariance model parameters related to the temporal delimitation of hydrographs/pollutographs and the intensity of the autocorrelation showed to have the strongest influence in the propagation of measurement errors (flattening/displacement of the PDFs).

Agricultural commodity price dynamics and their determinants: A comprehensive econometric approach

AbstractWe present a comprehensive modelling framework aimed at quantifying the response of agricultural commodity prices to changes in their potential determinants. The problem of model uncertainty is assessed explicitly by concentrating on specification selection based on the quality of short‐term out‐of‐sample forecasts (1 to 12 months ahead) for the price of wheat, soybeans and corn. Univariate and multivariate autoregressive models (autoregressive [AR], vector autoregressive [VAR] and vector error correction [VEC] specifications, estimated using frequentist and Bayesian methods), specifications with heteroskedastic errors (AR conditional heteroskedastic [ARCH] and generalized AR conditional heteroskedastic [GARCH] models) and combinations of these are entertained, including information about market fundamentals, macroeconomic and financial developments, and climatic variables. In addition, we assess potential non‐linearities in the commodity price dynamics along the business cycle. Our results indicate that variables measuring market fundamentals and macroeconomic developments (and, to a lesser extent, financial developments) contain systematic predictive information for out‐of‐sample forecasting of commodity prices and that agricultural commodity prices react robustly to shocks in international competitiveness, as measured by changes in the real exchange rate.

Uncertainty quantification and estimation of closed curves based on noisy data

Estimating closed curves based on noisy data has been a popular and yet a challenging problem in many fields of applications. Yet, uncertainty quantification of such estimation methods has received much less attention in the literature. The primary challenge stems from the fact that the parametrization of a closed curve is not generally unique and hence popular curve fitting methods (e.g., weighted least squares based on known parametrization) does not work well due to initialization instabilities leading to larger uncertainties. First, an initial set of cluster points are obtained by means of a constrained fuzzy c-means algorithm and an initial curve is constructed by fitting a B-spline curve based on the cluster centers. Second, a novel tuning parameter selection procedure is proposed to obtain optimal number of knots for the B-spline curve. Experimental results with simulated noisy data show that the proposed method works well for a variety of unknown closed curves with sharp changes of slopes and complex curvatures, even when moderate to large noises are added with heteroskedastic errors. Finally, a new curvature preserving uncertainty quantification method is proposed based on an adaptation of bootstrap method that provides confidence band around the fitted curve, an aspect that is rarely provided by popular curve fitting methods.

Vector Autoregressions with Dynamic Factor Coefficients and Conditionally Heteroskedastic Errors

Vector Autoregressions with Dynamic Factor Coefficients and Conditionally Heteroskedastic Errors

Highlighting Determinants of Financial Performance of the Jordanian Financial Sector: Panel Data Approach

This study was aimed at identifying the main determinants of financial performance in Jordanian financial sector over 2005-2016 periods. Profitability ratio (return on equity) was used as a proxy of financial performance measurement. Meanwhile, firms’ specific variables, macroeconomic variables and non-economic factors were used as explanation variables. Panel data set for four sub-sectors of financial sector over the above period were used. Pooled OLS, Fixed effect, random effects techniques with Heteroskedasticity and Serial Correlation Robust Standard Error estimation methods were employed. The empirical results showed that liquidity and leverage were the key determinants of financial performance while risk, macroeconomic factors and non-economic factors do not affect the financial performance of financial sector in Amman Stock Exchange. Therefore, the results conclude that financial performance is mainly driven by firm specific factors (company characteristics). Thus, a sound financial performance can be obtained by giving attention to firm specific variables.

Contagion between real estate and financial markets: A Bayesian quantile-on-quantile approach

We study contagion between Real Estate Investment Trusts (REITs) and the equity market in the U.S. over four sub-samples covering January, 2003 to December, 2017, by using Bayesian nonparametric quantile-on-quantile (QQ) regressions with heteroskedasticity. We find that the spillovers from the REITs on to the equity market has varied over time and quantiles defining the states of these two markets across the four sub-samples, thus providing evidence of shift-contagion. Further, contagion from REITs upon the stock market went up during the global financial crisis particularly, and also over the period corresponding to the European sovereign debt crisis, relative to the pre-crisis period. Our main findings are robust to alternative model specifications of the benchmark Bayesian QQ model, especially when we control for omitted variable bias using the heteroskedastic error structure. Our results have important implications for various agents in the economy namely, academics, investors and policymakers.

Modeling Cross-National Differences in Automated Vehicle Acceptance

The technology that allows fully automated driving already exists and it may gradually enter the market over the forthcoming decades. Technology assimilation and automated vehicle acceptance in different countries is of high interest to many scholars, manufacturers, and policymakers worldwide. We model the mode choice between automated vehicles and conventional cars using a mixed multinomial logit heteroskedastic error component type model. Specifically, we capture preference heterogeneity assuming a continuous distribution across individuals. Different choice scenarios, based on respondents’ reported trip, were presented to respondents from six European countries: Cyprus, Hungary, Iceland, Montenegro, Slovenia, and the UK. We found that large reservations towards automated vehicles exist in all countries with 70% conventional private car choices, and 30% automated vehicles choices. We found that men, under the age of 60, with a high income who currently use private car, are more likely to be early adopters of automated vehicles. We found significant differences in automated vehicles acceptance in different countries. Individuals from Slovenia and Cyprus show higher automated vehicles acceptance while individuals from wealthier countries, UK, and Iceland, show more reservations towards them. Nontrading mode choice behaviors, value of travel time, and differences in model parameters among the different countries are discussed.

Estimation and inference for spatial models with heterogeneous coefficients: An application to US house prices

SummaryThis paper considers the estimation and inference of spatial panel data models with heterogeneous spatial lag coefficients, with and without weakly exogenous regressors, and subject to heteroskedastic errors. A quasi maximum likelihood (QML) estimation procedure is developed and the conditions for identification of the spatial coefficients are derived. The QML estimators of individual spatial coefficients, as well as their mean group estimators, are shown to be consistent and asymptotically normal. Small‐sample properties of the proposed estimators are investigated by Monte Carlo simulations and results are shown to be in line with the paper's key theoretical findings, even for panels with moderate time dimensions and irrespective of the number of cross‐section units. A detailed empirical application to US house price changes during the 1975–2014 period shows a significant degree of heterogeneity in spatiotemporal dynamics over the 338 Metropolitan Statistical Areas considered.